This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann–Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.
In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.
Sample Chapter(s)
Preface
Chapter 1: Preliminaries
Contents:
- Preliminaries
- Riemann–Liouville Fractional Differential Equations with Nonlocal Boundary Conditions
- Systems of Two Riemann–Liouville Fractional Differential Equations with Multi-Point Boundary Conditions
- Systems of Two Riemann–Liouville Fractional Differential Equations with p-Laplacian Operators, Parameters and Multi-Point Boundary Conditions
- Systems of Three Riemann–Liouville Fractional Differential Equations with Parameters and Multi-Point Boundary Conditions
- Existence of Solutions for Riemann–Liouville Fractional Boundary Value Problems
- Existence of Solutions for Caputo Fractional Boundary Value Problems
Readership: Mathematical and scientific researchers, and graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.
Bashir Ahmad is Full Professor of Mathematics at King Abdulaziz University, Jeddah, Saudi Arabia. He received his PhD degree from Quaid-i-Azam University, Islamabad, Pakistan in 1995. His research interest includes approximate/numerical methods for nonlinear problems involving a variety of differential equations, existence theory of fractional differential equations, stability and instability properties of dynamical systems, impulsive systems, and fluid mechanics. He was honored with the "Best Researcher of King Abdulaziz University" Award in 2009. He has supervised the theses of 7 PhD and 22 MPhil/MS students. He has published 2 books and more than 500 research articles in JCR journals, including 29 highly cited articles in the field. He is Managing Editor of the journal Bulletin of Mathematical Sciences and is member of editorial boards of several journals. He has been a "Highly-Cited Researcher" in the category of Mathematics since 2014. He was listed in the top 1% of reviewers in Mathematics on Publons for the 2018 and 2019 global Peer Review Awards.
Johnny Henderson has served as Distinguished Professor of Mathematics at Baylor University since 2002. He received his PhD in mathematics from the University of Nebraska-Lincoln in 1981. He was Assistant Professor of Mathematics at Missouri University of Science and Technology for 3 years, after which for 18 years he served on the faculty at Auburn University, first holding the position of Alumni Professor of Mathematics followed by the position of Scharnagel Professor of Mathematics. He was named as an Inaugural "Fellow of the American Mathematical Society" in 2013, and in 2016, he was honored as the "Cornelia Marschall Smith Professor of the Year" by Baylor University. He has co-authored 9 books and over 600 published papers. He has directed the dissertations of 27 doctoral students. His areas of research include nonlinear boundary value problems for ordinary differential equations, for finite difference equations, for dynamic equations on time scales, and for fractional differential equations.
Rodica Luca is Full Professor of Mathematics at "Gheorghe Asachi" Technical University of Iasi, Romania. She received her PhD in mathematics from "Alexandru Ioan Cuza" University of Iasi in 1996, and her Habilitation Certificate in mathematics from the School of Advanced Studies of the Romanian Academy, Bucharest in 2017. She received the "Spiru Haret" Prize of the Romanian Academy in 2018 for her book published by Elsevier in 2016, written in collaboration with Professor Johnny Henderson, and 29 prizes in the "National Research, Development and Innovation Plan — Awards for Research Results" program for her papers. She has published more than 160 papers. Her research interests are boundary value problems for nonlinear systems of ordinary differential equations, finite difference equations, and fractional differential equations, and initial-boundary value problems for nonlinear hyperbolic systems.
